We assume a randomized experiment on \(N\)  units, and let \(X \in \lbrace 0,1\rbrace ^N\)  denote the treatment assignment, \(Y\in \lbrace 0,1\rbrace ^N\)  the observed outcomes, and \(\theta \in \lbrace 0,1\rbrace ^N\)  the counterfactual outcomes that would result under a “uniformity trial” [1]}. Under the uniformity trial, the random treatment assignment \(X\)  is generated but not actually administered, so that the outcomes are unaffected by it. A common choice of uniformity trial is to let \(\theta \)  denote the outcomes if all units were to receive the control regardless of \(X\) .
